Finite Group Databasebeta

← #11069510

Subgroups — #11069510

Order 768.

2624 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5494C212yesmaximal, complemented
2C2×C3×#390C211yesmaximal, characteristic, complemented
3#84053C212yesmaximal, complemented
4C4⋊C4×#67C212yesmaximal, complemented
5#82128C214yesmaximal, complemented
6#82117C212yesmaximal, complemented
7#82076C211yesmaximal, characteristic, complemented
8C4×#930C211yesmaximal, characteristic, complemented
9#76470C214yesmaximal, complemented
10#76466C212yesmaximal, complemented
11#76452C212yesmaximal, complemented
12#76439C212yesmaximal, complemented
13#76399C212yesmaximal, complemented
14#76339C212yesmaximal, complemented
15#76335C212yesmaximal, complemented
16#39375—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C42C2211yescharacteristic
22C2×#953C2214yes—
23C2×#938C2212yes—
24C2×#938C2212yes—
25C2×#930C2211yescharacteristic
26C2×C4×#67C2212yes—
27C2×C4×#67C2214yes—
28C2×#924C2212yes—
29C2×D3×C4⋊C4C2212yescomplemented
30#5494—216no—
31C2×#885C2214yescomplemented
32C2×#884C2214yescomplemented
33C2×#883C2214yescomplemented
34C2×#883C2214yescomplemented
35C2×#879C2214yescomplemented
36C2×C4×D12C2211yescharacteristic, complemented
37C2×#869C2211yescharacteristic, complemented
38C3×#390C2212yes—
39C3×#390C2212yes—
40C3×#390C2212yes—
41C3×#390C2212yes—
42#5247C2214yes—
43#5223C2214yes—
44#5222C2214yes—
45#5221C2212yes—
46#5221C2212yes—
47#5213C2212yes—
48#5212C2212yes—
49#5212C2211yescharacteristic
50#5212C2212yes—
51#5210C2214yes—
52#4989C2214yescomplemented
53#4987C2212yescomplemented
54#4976C2214yescomplemented
55#4975C2212yescomplemented
56Dic3×C4⋊C4C2212yescomplemented
57#4961C2214yescomplemented
58#4959C2214yescomplemented
59#4956C2214yescomplemented
60#4952C2214yescomplemented
61#4951C2214yescomplemented
62#4949C2214yescomplemented
63#4949C2214yescomplemented
64#4948C2214yescomplemented
65#4948C2214yescomplemented
66#4947C2214yescomplemented
67#4945C2214yescomplemented
68#4940C2212yescomplemented
69#4939C2211yescharacteristic, complemented
70C4×(C2×D3)⋊C4C2212yescomplemented
71#4935C2211yescharacteristic, complemented
72C4×C4⋊Dic3C2211yescharacteristic, complemented
73#4929C2212yescomplemented
74#4928C2212yescomplemented
75#4928C2211yescharacteristic, complemented
76#4928C2212yescomplemented
77C2×#538—32no—
78#2857—31no—
79#2727—32no—
80#2710—34no—
81#2682—32no—
82#2626—32no—
83#2512—32no—
84#2501—32no—
85#2491—32no—
86#2418—34no—
87#2416—32no—
88#2408—32no—
89D4×C4⋊C4—32no—
90C4×#121—31no—
91C2×#390D311yescharacteristic, complemented
92C25×C3C2312yes—
93C22×C3×D4—24no—
94C22×C3×D4—42no—
95C22×C3×D4—42no—
96C22×C3×D4C2312yes—
97C22×C3×D4C2312yes—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2312yes—
101C23×C3×C4C2311yescharacteristic
102C22×#67C2312yes—
103C22×#67C2314yes—
104C22×#67C2314yes—
105C22×D12C2311yescharacteristic
106C22×C4×D3C2312yes—
107C22×C4×D3C2314yes—
108C22×Dic6C2312yes—
109C2×C3×C4⋊C4—42no—
110C2×C3×C4⋊C4C2312yes—
111C2×C3×C4⋊C4C2312yes—
112C2×C3×C22⋊C4—28no—
113C2×C3×C22⋊C4—44no—
114C2×C3×C22⋊C4C2314yes—
115C2×C3×C22⋊C4C2314yes—
116C2×C3×C22⋊C4C2314yes—
117C2×C3×C22⋊C4C2314yes—
118C2×C3×C42—42no—
119C2×C3×C42C2311yescharacteristic
120C2×C3×C42C2311yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123#953—216no—
124C2×#217C2314yes—
125C2×#217C2314yes—
126C2×#217C2312yes—
127C2×#217C2314yes—
128C2×#217C2314yes—
129C2×#217C2314yes—
130C2×#217C2314yes—
131C2×#217C2314yes—
132#938—44no—
133#938—44no—
134#930D418yescomplemented
135C4×#67—28no—
136C4×#67—216no—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×C4⋊Dic3C2312yes—
143C2×C4⋊Dic3C2312yes—
144C2×C4⋊Dic3C2312yes—
145C2×C4⋊Dic3C2312yes—
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150#924—28no—
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2312yes—
153C2×Dic3⋊C4C2314yes—
154C2×Dic3⋊C4C2314yes—
155C2×Dic3⋊C4C2314yes—
156C2×C4×Dic3C2312yes—
157C2×C4×Dic3C2314yes—
158D3×C4⋊C4—44no—
159#885—216no—
160#884—216no—
161#883—216no—
162#883—48no—
163#879—216no—
164C4×D12—42no—
165#869—42no—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2312yes—
169C3⋊#95C2312yes—
170C3⋊#95C2312yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C23×D4C2×D311yescharacteristic
174#538—616no—
175C2×C4⋊Q8—31no—
176C2×#126—34no—
177C2×#124—34no—
178C2×#123—34no—
179C2×#123—34no—
180C2×C22⋊Q8—32no—
181C2×#121—31no—
182C2×#121—32no—
183C2×#121—32no—
184C2×#121—34no—
185C2×#120—34no—
186C2×C4×D4—32no—
187C2×C4×D4—34no—
188C2×C4×D4—31no—
189C22×C4⋊C4—32no—
190C22×C4⋊C4C2×D311yescharacteristic
191C22×C22⋊C4C2×D312yes—
192C22×C22⋊C4C2×D312yes—
193C22×C42C2×D311yescharacteristic
194#399—34no—
195#399—34no—
196#397—34no—
197#396—34no—
198#396—34no—
199#394—34no—
200#394—34no—
201#394—34no—
202#393—34no—
203#392—34no—
204#391—32no—
205#390—32no—
206#390—32no—
207#390—31no—
208#390C2×D312yes—
209#390C2×D312yes—
210#390C2×D312yes—
211#390C2×D312yes—
212#389—34no—
213#389—32no—
214#389—32no—
215#389—31no—
216#388—34no—
217#388—34no—
218#388—32no—
219#386—32no—
220#386—34no—
221#385—34no—
222#385—34no—
223#384—32no—
224#384—31no—
225#380—32no—
226#380—32no—
227#380—31no—
228#380—32no—
229#379—34no—
230C4×C4⋊C4—32no—
231C4×C4⋊C4—31no—
232C4×C22⋊C4—32no—
233C24×C3—24no—
234C24×C3—24no—
235C24×C3—24no—
236C24×C3—42no—
237C24×C3—42no—
238C24×C3—42no—
239C24×C3—42no—
240C24×C3C2414yes—
241C24×C3C2411yescharacteristic
242C23×D3C2412yes—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—24no—
247C2×C3×D4—42no—
248C2×C3×D4—42no—
249C2×C3×D4—416no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—24no—
254C22×C3×C4—22no—
255C22×C3×C4—41no—
256C22×C3×C4—41no—
257C22×C3×C4—41no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4C2×D414yes—
261C22×C3×C4#4114yes—
262C22×C3×C4C2411yescharacteristic
263C22×C3×C4C2414yes—
264C22×C3×C4C2411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C2×#67—24no—
270C2×#67—24no—
271C2×#67—28no—
272C2×#67—28no—
273C2×#67—44no—
274C2×#67—44no—
275C2×#67—44no—
276C2×#67—44no—
277C2×#67C2×D418yes—
278C22×Dic3C2412yes—
279C22×Dic3C2414yes—
280C22×Dic3C2412yes—
281C22×Dic3C2414yes—
282C22×Dic3C2412yes—
283C2×D12—41no—
284C2×D12—41no—
285C2×D12C2×D414yescomplemented
286C2×C4×D3—24no—
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—28no—
290C2×C4×D3—44no—
291C2×C4×D3—44no—
292C2×Dic6—24no—
293C2×Dic6—42no—
294C2×Dic6—42no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—42no—
297C3×C22⋊C4—28no—
298C3×C22⋊C4—28no—
299C3×C22⋊C4—28no—
300C3×C22⋊C4—44no—
301C3×C42—22no—
302C3×C42—22no—
303C3×C42—41no—
304C3×C42—41no—
305#217—28no—
306#217—24no—
307#217—28no—
308#217—28no—
309#217—44no—
310#217—44no—
311#217—44no—
312#217—44no—
313(C2×D3)⋊C4—28no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—42no—
317(C2×D3)⋊C4C2×D418yescomplemented
318C4⋊Dic3—24no—
319C4⋊Dic3—24no—
320C4⋊Dic3—24no—
321C4⋊Dic3—24no—
322C4⋊Dic3—42no—
323C4⋊Dic3—41no—
324C4⋊Dic3—41no—
325C4⋊Dic3C2×D414yescomplemented
326Dic3⋊C4—28no—
327Dic3⋊C4—24no—
328Dic3⋊C4—28no—
329Dic3⋊C4—44no—
330Dic3⋊C4—44no—
331C4×Dic3—24no—
332C4×Dic3—28no—
333C25C22×D312yes—
334C22×Q8—32no—
335C22×D4—24no—
336C22×D4—32no—
337C22×D4—34no—
338C22×D4—34no—
339C22×D4—31no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4C22×D312yes—
343C22×D4C22×D312yes—
344C23×C4—32no—
345C23×C4—34no—
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D312yes—
349C23×C4C22×D311yescharacteristic
350C4⋊Q8—122no—
351#126—616no—
352#124—616no—
353#123—616no—
354#123—128no—
355C22⋊Q8—68no—
356#121—38no—
357#121—616no—
358#121—124no—
359#121—124no—
360#120—616no—
361C4×D4—616no—
362C4×D4—68no—
363C4×D4—122no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—32no—
366C2×C4⋊C4—34no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—34no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—34no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—34no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—124no—
379C2×C4⋊C4C22×D312yes—
380C2×C4⋊C4C22×D312yes—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—34no—
387C2×C22⋊C4—34no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—34no—
391C2×C22⋊C4—34no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4C22×D314yes—
397C2×C22⋊C4C22×D314yes—
398C2×C22⋊C4C22×D314yes—
399C2×C22⋊C4C22×D314yes—
400C2×C42—34no—
401C2×C42—32no—
402C2×C42—42no—
403C2×C42C22×D311yescharacteristic
404C2×C42C22×D311yescharacteristic
405C2×C42C22×D311yescharacteristic
406C2×C42C22×D311yescharacteristic
407#95—32no—
408#95—32no—
409#95—34no—
410#95—32no—
411#95—34no—
412#95—34no—
413#95—34no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—48no—
426C23×C3—48no—
427C23×C3—48no—
428C23×C3—84no—
429C23×C3—84no—
430C23×C3—84no—
431C23×C3—84no—
432C23×C3C22×D412yes—
433C23×C3C2×#4112yes—
434C23×C32−1+412yes—
435C23×C3C2511yescharacteristic
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3C22×D414yes—
443C3×D4—48no—
444C3×D4—48no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—28no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—44no—
461C2×C3×C4—44no—
462C2×C3×C4—84no—
463C2×C3×C4C22×D412yes—
464C2×C3×C4C22×D412yes—
465C2×C3×C4C2×#4112yes—
466C2×C3×C4C2×#4112yes—
467C2×C3×C4H(5,𝔽2)12yes—
468C2×C3×C4H(5,𝔽2)12yes—
469C2×C3×C4H(5,𝔽2)12yes—
470#67—216no—
471#67—88no—
472#67—88no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—24no—
476C2×Dic3—24no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—24no—
482C2×Dic3—24no—
483C2×Dic3—24no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—24no—
487C2×Dic3C22×D414yes—
488D12—44no—
489C4×D3—48no—
490C4×D3—88no—
491Dic6—84no—
492C24—24no—
493C24—24no—
494C24—24no—
495C24—32no—
496C24—42no—
497C24—42no—
498C24—42no—
499C24—42no—
500C24C23×D314yes—
501C24C23×D311yescharacteristic
502C2×Q8—64no—
503C2×Q8—122no—
504C2×Q8—122no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—38no—
510C2×D4—34no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—416no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—68no—
517C2×D4—68no—
518C2×D4—121no—
519C2×D4—121no—
520C2×D4—124no—
521C2×D4—124no—
522C2×D4—124no—
523C2×D4—124no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—34no—
532C22×C4—32no—
533C22×C4—34no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—68no—
540C22×C4—64no—
541C22×C4—64no—
542C22×C4—64no—
543C22×C4—124no—
544C22×C4—124no—
545C22×C4#23514yes—
546C22×C4D3×D414yes—
547C22×C4C23×D311yescharacteristic
548C22×C4C23×D314yes—
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D311yescharacteristic
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D311yescharacteristic
554C4⋊C4—24no—
555C4⋊C4—34no—
556C4⋊C4—42no—
557C4⋊C4—68no—
558C4⋊C4—64no—
559C4⋊C4—68no—
560C4⋊C4—64no—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—64no—
564C4⋊C4—124no—
565C4⋊C4—121no—
566C4⋊C4—124no—
567C4⋊C4—122no—
568C4⋊C4—121no—
569C22⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—28no—
572C22⋊C4—38no—
573C22⋊C4—44no—
574C22⋊C4—68no—
575C22⋊C4—68no—
576C22⋊C4—68no—
577C22⋊C4—64no—
578C22⋊C4—68no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—122no—
582C22⋊C4—124no—
583C22⋊C4—124no—
584C22⋊C4—124no—
585C22⋊C4—124no—
586C42—22no—
587C42—22no—
588C42—41no—
589C42—41no—
590C42—68no—
591C42—64no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—816no—
606C22×C3#54714yes—
607C22×C3C23×D411yescharacteristic
608C22×C3C22×#4111yescharacteristic
609C22×C3C2×H(5,𝔽2)11yescharacteristic
610C22×C3C2×H(5,𝔽2)11yescharacteristic
611C22×C3C2×H(5,𝔽2)11yescharacteristic
612C22×C3C2×2−1+411yescharacteristic
613C22×C3#58511yescharacteristic
614C2×D3—24no—
615C2×D3—24no—
616C2×D3—24no—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—44no—
626C3×C4—41no—
627C3×C4#53814yescomplemented
628Dic3—24no—
629Dic3—42no—
630Dic3—44no—
631Dic3—44no—
632Dic3—42no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—34no—
645C23—48no—
646C23—48no—
647C23—48no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23C2×#23512yes—
659C23C2×D3×D412yes—
660C23#101012yes—
661C23C24×D311yescharacteristic
662Q8—244no—
663D4—48no—
664D4—48no—
665D4—616no—
666D4—124no—
667D4—248no—
668D4—248no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—28no—
678C2×C4—24no—
679C2×C4—21no—
680C2×C4—24no—
681C2×C4—21no—
682C2×C4—24no—
683C2×C4—21no—
684C2×C4—34no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—64no—
697C2×C4—64no—
698C2×C4—64no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—84no—
702C2×C4—128no—
703C2×C4—248no—
704C2×C4C2×#23512yes—
705C2×C4C2×#23512yes—
706C2×C4C2×D3×D412yes—
707C2×C4C2×D3×D412yes—
708C2×C4#100412yes—
709C2×C4#100412yes—
710C2×C4#100412yes—
711C2×C3—24no—
712C2×C3—84no—
713C2×C3C2×#53811yescharacteristic
714C2×C3C2×#54711yescharacteristic
715C2×C3#349611yescharacteristic
716C2×C3#349811yescharacteristic
717C2×C3#350611yescharacteristic
718C2×C3#353611yescharacteristic
719C2×C3#356111yescharacteristic
720D3—44no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—64no—
735C22—64no—
736C22—64no—
737C22—816no—
738C22—122no—
739C22—122no—
740C22—122no—
741C22—122no—
742C22#555114yes—
743C22C22×#23511yescharacteristic
744C22C22×D3×D411yescharacteristic
745C22C2×#100411yescharacteristic
746C22C2×#100411yescharacteristic
747C22C2×#100411yescharacteristic
748C22C2×#101011yescharacteristic
749C22#596411yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—44no—
755C4—41no—
756C4—64no—
757C4—122no—
758C4—124no—
759C4—124no—
760C4—122no—
761C4#549414yescomplemented
762C3#3937511yescharacteristic, complemented, Sylow
763C2—24no—
764C2—84no—
765C2—124no—
766C2C2×#549411yescharacteristic
767C2C2×#555111yescharacteristic
768C2#8578811yescharacteristic
769C2#8595011yescharacteristic
770C2#8595511yescharacteristic
771C2#8608111yescharacteristic
772C2#8619511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#390C2
hypercenterC2×#390D3
hypocenterC3#39375
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#390

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#5494C2semidirect
2. C2×C3×#390C2semidirect
3. #84053C2semidirect
4. C4⋊C4×#67C2semidirect
5. #82128C2semidirect
6. #82117C2semidirect
7. #82076C2semidirect
8. C4×#930C2semidirect
9. #76470C2semidirect
10. #76466C2semidirect
11. #76452C2semidirect
12. #76439C2semidirect
13. #76399C2semidirect
14. #76339C2semidirect
15. #76335C2semidirect
29. C2×D3×C4⋊C4C22semidirect
31. C2×#885C22semidirect
32. C2×#884C22semidirect
33. C2×#883C22semidirect
34. C2×#883C22semidirect
35. C2×#879C22semidirect
36. C2×C4×D12C22semidirect
37. C2×#869C22semidirect
52. #4989C22semidirect
53. #4987C22semidirect
54. #4976C22semidirect
55. #4975C22semidirect
56. Dic3×C4⋊C4C22semidirect
57. #4961C22semidirect
58. #4959C22semidirect
59. #4956C22semidirect
60. #4952C22semidirect
61. #4951C22semidirect
62. #4949C22semidirect
63. #4949C22semidirect
64. #4948C22semidirect
65. #4948C22semidirect
66. #4947C22semidirect
67. #4945C22semidirect
68. #4940C22semidirect
69. #4939C22semidirect
70. C4×(C2×D3)⋊C4C22semidirect
71. #4935C22semidirect
72. C4×C4⋊Dic3C22semidirect
73. #4929C22semidirect
74. #4928C22semidirect
75. #4928C22semidirect
76. #4928C22semidirect
91. C2×#390D3semidirect
134. #930D4semidirect
285. C2×D12C2×D4semidirect
317. (C2×D3)⋊C4C2×D4semidirect
325. C4⋊Dic3C2×D4semidirect
627. C3×C4#538semidirect
761. C4#5494semidirect
762. C3#39375semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#54942
C2×C3×#3902
#840532
C4⋊C4×#672
#821282
#821172
#820762
C4×#9302
#764702
#764662
#764522
#764392
#763992
#763392
#763352
#393753